1 / 17

Section 13.2: Recursive Definitions

Section 13.2: Recursive Definitions. Pre-Calculus. Learning Targets. Write a recursive definition for a sequence Compare and contrast recursive definitions and explicit definitions. Can you figure out the pattern?. 1, 1, 2, 3, 5, 8, 13, 21, … What is the next number?.

loan
Télécharger la présentation

Section 13.2: Recursive Definitions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 13.2: Recursive Definitions Pre-Calculus

  2. Learning Targets • Write a recursive definition for a sequence • Compare and contrast recursive definitions and explicit definitions

  3. Can you figure out the pattern? • 1, 1, 2, 3, 5, 8, 13, 21, … • What is the next number?

  4. 1, 1, 2, 3, 5, 8, 13, 21, … • To find the next number in the sequence, we had to know the previous numbers. • This idea is called a recursive definition

  5. Recursive Definition • A definition of a sequence that consists of • An initial condition to indicate the start of the sequence • A formula that relates how any term in the sequence is related to the preceding term

  6. Recursive Definition • For example,

  7. Recursive Definition VS Explicit definition

  8. Example 1: Finding the next terms in the sequence • Given find the next 3 terms in the sequence • Is it possible to write an explicit formula for this sequence? If so, what is it?

  9. Example 2:WRite a recursive definition • For the sequence: 1, 2, 6, 24, 120, 720, …

  10. Example 3:WRite a recursive definition • For the sequence: 3, 6, 12, 24, …

  11. Example 4:WRite a recursive definition • For the sequence: 4, 7, 13, 25, …

  12. Example 5:WRite a recursive definition • for the sequence: 10, 12, 15, 19, …

  13. Example 6:WRite a recursive definition • For the sequence: 1, 1, 2, 3, 5, 8, 13, 21, …

  14. Fibonacci Sequence One of the most FAMOUS sequences of all time! It generates the golden ratio which is believed to be the “ratio of god” and is very evident in the world around us. The golden ratio is produced by dividing any number in the sequence by its preceding term

  15. Fibonacci Sequence • It is used in • Graphic Design • Art • Music • Architecture • Photography • Personal Beauty • Stock Market Analysis

  16. Fibonacci SEquence http://www.youtube.com/watch?v=0tAZe6pP-FM

  17. Homework • Textbook pg 481: #1-3, 12, 13-17odd

More Related